OFFSET
1,5
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 antidiagonals)
FORMULA
G.f. of column k: Sum_{j>=1} prime(j)^k*x^prime(j)/(1 - x^prime(j)).
EXAMPLE
Square array begins:
0, 0, 0, 0, 0, 0, ...
1, 2, 4, 8, 16, 32, ...
1, 3, 9, 27, 81, 243, ...
1, 2, 4, 8, 16, 32, ...
1, 5, 25, 125, 625, 3125, ...
2, 5, 13, 35, 97, 275, ...
MATHEMATICA
Table[Function[k, Sum[Boole[PrimeQ[d]] d^k, {d, Divisors[n]}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
Table[Function[k, SeriesCoefficient[Sum[Prime[j]^k x^Prime[j]/(1 - x^Prime[j]), {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
PROG
(PARI) T(n, k)={vecsum([p^k | p<-factor(n)[, 1]])}
for(n=1, 10, for(k=0, 8, print1(T(n, k), ", ")); print); \\ Andrew Howroyd, Nov 26 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Nov 26 2018
STATUS
approved